Can the total number of stocks in a company change?

I was discussing doing some work for shares in a startup when the owner mentioned something interesting.

Basically I would be given X shares for my work and with the current number of stock that came out to 1% of the total stock, BUT as investors come on this percentage will decrease.

Does this mean that more stock can be created? Could the company just create a billion more shares and render mine essentially worthless?

Basically I would be given X shares for my work and with the current number of stock that came out to 1% of the total stock, BUT as investors come on this percentage will decrease.
Does this mean that more stock can be created?

Yes. In fact, that is precisely what happens in subsequent rounds of investment.

Could the company just create a billion more shares and render mine essentially worthless?

Yes. Protecting against the majority shareholders creating more new shares
and awarding these shares to themselves is usually done in a Shareholder's Agreement, or sometimes the company bylaws, or sometimes provisions buried somewhere else in all the legal paperwork. If you don't have a clause somewhere which clearly protects against this issue, then you're at some risk of it happening.

There is IMHO a meme going around about "non-diluteable shares". There is no such thing, it's a false meme propagated by a certain movie. You can have a non-dilution clause somewhere, but be aware that this can be highly disadvantageous for new investors, and can mean you outright loose access to vital outside investment.

Yes, and Yes.

Corporations always have the ability to issue more stock. There are also several different kinds of stock they can issue.

One way to protect your ownership stake in a company is to have a non-dilution clause in your equity contract. Or at least some sort of stock option that allowed you to have first shot at any newly issued shares. This would require you to contribute more funds to the company in the form of a stock purchase to protect your ownership share, but would at least offer some protection from dilution.